Ratio of two adjacent sides of a parallelogram is $3 : 4,$ and its perimeter is $112 c m$ . Find the length of its each side.

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Solution

Let the two sides be $3 x$ and $4 x$ .
In a parallelogram the opposite sides are congruent.
So, the sides are $3 x, 3 x, 4 x$ and $4 x$
Perimeter $= 112 c m$
$3 x + 3 x + 4 x + 4 x = 112$
$\Rightarrow 14 x = 112$
$\Rightarrow x = \frac{112}{14}$
$\Rightarrow x = 8$
So $3 x = 3 \times 8 = 24 c m$
$4 x = 4 \times 8 = 32 c m$
Thus, the sides are $24 c m, 32 c m, 24 c m$ and $32 c m$ .

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